MAT1322 IMAGE

5 Q12. Let R be the region that lies between the curve 3; = 13\" and the I-axis on the interval [6,00]. 5 . . _ The graph of y = m is given here. no (a) [2 points] The area of R corresponds to the improper integral / % dz. 6 Determine whether this improper integral converges or diverges. If it converges, nd its exact value. Your answer must be wellvjustilied. (b) [1 point] Let S be the solid obtained by revolving R about the :r-axis. Give an expremion for the approximate volume V(:c) of the thin slice of S that lie; between I and 1+ AI, where its thickness As: is assumed to be small. (c) [3 points] Give an improper integral that computes the volume of S and determine whether it converges or diverges. If it converges, nd the exact volume of S. Your answer must be well-justied and use appropriate mathematical notation